STRUCTURE OF EXPANDED LIQUID RUBIDIUM BY NEUTRON DIFFRACTION

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STRUCTURE OF EXPANDED LIQUID RUBIDIUM

BY NEUTRON DIFFRACTION

G. Franz, W. Freyland, W. Gläser, F. Hensel, E. Schneider

To cite this version:

JOURNAL DE PHYSIQUE _CoZZoque C8, suppZe'ment au n08, Tome 4 7 , aoiit 1980, page C8-194

STRUCTURE OF EXPANDED L I Q U I D RUBIDIUF1 BY NEUTRON DIFFRACTION

G. Franz, W. Freyland, W. ~ l i s e r + , F. Hensel and E. Schneider +

Fachbereich Physikalische Chemie, PhiZipps-Uni~ersitBt Hans-Meemein-Strasse, 0-3550, Marburg, R.F.A. f

Physik Department E 2 1 , Technische U n i v e r s i t a t Miinchen, 0-8046 Garching, R.F.A.

Abstract.- The static structure factor, S(Q), of liquid rubidium has been studied by neutron diffrac- tion for temperatures up to 2000 K and pressures up to 139 bar near saturation conditions, corres- ponding to an expansion of the liquid from 1.46 to 0.54 gcm-3. The characteristic changes of the scattering behaviour and of the microscopic structure approaching the M-NM transition region are dis- cussed. A comparison of these results with simple hard sphere model calculations is given.

I IKTRODUCT ION F l u i d a l k a l i m e t a l s show o v e r a r e l a t i v e l y w i d e r a n g e o f e x p a n s i o n t y p i c a l m e t a l l i c b e h a v i o u r i n t h e i r e l e c t r i c a l t r a n s p o r t p r o p e r t i e s , c o n s i s t c n t w i t h a n e a r l y f r e e e l e c t r o n d e s c r i p t i o n

-

s c e e . g . ( I ) , ( 2 )

-.

However, f o r d e n s i t i e s n e a r d o u b l e t h e c r i t i c a l d e n s i t y and c o n d i t i o n s n e a r t h e s a t u r a t i o n c u r v e , c h a r a c t e r i s t i c c h a n g e s a r e o b s e r v e d f o r b o t h t h e e l e c t r i c a l and m a g n e t i c p r o p e r t i e s ( 3 )

,

( 4 ) , ( 5 )

,

m a r k i n g t h e o n s e t o f a t r a n s i t i o n from m e t a l l i c t o n o n m e t a l l i c s t a t e s ( 6 ) . T h i s s t r o n g l y i n - f l u e n c e s t h e n a t u r e o f t h e e l e c t r o n i c s t a t e s a n d , a p p a r e n t l y , r e q u i r e s a t r a n s - f o r m a t i o n o f t h e i n t e r m o l e c u l a r i n t e r a c - t i o n . I n r e l a t i o n t o t h e s e p r o b l e m s e x p e - r i m e n t a l i n f o r m a t i o n on t h e c o r r e s p o n d i n g v a r i a t i o n o f t h c m i c r o s c o p i c s t r u c t u r e i s i m p o r t a n t . Y a i n l y two q u c s t i o n s a r e o f s p e c i a l i n t e r e s t h e r e a n d t h e s e c o n c e r n : 1 ) t h e c h a n g e o f t h e l o c a l s t r u c t u r e i n t h e e x p a n d e d m e t a l l i c l i q u i d i n c o m p a r i s o n t o t h a t n e a r t h e m e l t i n g p o i n t ; 2 ) s p e c i f i c d i f f e r e n c e s o r s i m i l a r i t i e s o f t h e s c a t t e r i n g b e h a v i o u r i n t h e I\!-NM t r a n - s i t i o n r e g i o n i n c o m p a r i s o n w i t h o t h e r s i m p l c l i q u i d s , l i k e L e n n a r d - J o n e s f l u i d s . F o r t h e s e r e a s o n s we h a v e e x t e n d e d t h e i n - v e s t i g a t i o n o f t h e s t a t i c s t r u c t u r e f a c t o r , S ( Q ) , o f e x p a n d e d l i q u i d r u b i d i u m f o r c o n - d i t i o n s n e a r t h e c r i t i c a l p o i n t (Tc = 2090 K , pc = 14 5 b a r and p c = 0 . 3 3 gcm-3)

.

I n t h i s p a p e r new r e s u l t s a r e p r e s e n t e d u p t o 2000 K a n d a c o r r e s p o n d i n g d e n s i t y o f 0 . 5 4 . g ~ r n - ~ , c o m p l e t i n g o u r p r e v i o u s s t u d y o n r u b i d i u m ( 7 ) .

I I DATA COR!IECT ION AKD EIIROR EST IPIATE The n e u t r o n d i f f r a c t i o n e x p e r i m e n t h a s b e e n c a r r i e d o u t a t t h e s p e c t r o m c t e r D I B o f t h e h i g h f l u x r e a c t o r a t G r e n o b l e . The h i g h t e m p e r a t u r e - h i g h p r e s s u r e s e t up u s e d f o r t h i s i n v e s t i g a t i o n h a s b e e n d e s c r i b e d i n a p r e v i o u s p a p e r ( 7 ) , w h i c h a l s o c o n t a i n s f u r t h e r e x p e r i m e n t a l d e t a i l s . I n t h e f o l l o - wing o n l y t h a t p a r t o f t h e d a t a c o r r e c t i o n w i l l b e o u t l i n e d , w h i c h i s s p e c i f i c f o r t h i s e x p e r i m e n t , i . e . t h e b a c k g r o u n d s c a t - t e r i n g a n d a b s o r p t i o n d u e t o t h e h i g h p r e s - s u r e f u r n a c e . A b r i e f e s t i m a t e o f t h e u n - c e r t a i n t y o f t h e f i n a l S ( Q ) - d a t a w i l l b e d i s c u s s e d .

I n a n i d e a l c a s e , when m e a s u r e m e n t s c a n be p e r f o r m e d u n d e r vacuum, t h e s c a t t e r i n g i n - t e n s i t y o f t h e l i q u i d s a m p l e a l o n e , I s , i s g i v e n by

-

s e e e . g . ( 8 )

-

w h e r e I : + ~ a n d 1: d e n o t e t h e e x p e r i m e n t a l i n t e n s i t i e s o f s a m p l e p l u s c o n t a i n e r and empty c o n t a i n e r , r e s p e c t i v e l y . The A i , k a r e t h e a b s o r p t i o n c o e f f i c i e n t s i n t r o d u c e d by Paalmann a n d P i n g s ( 8 ) . I n t h e p r e s e n t e x p e r i m e n t , t h e c o r r e s p o n d i n g i n t e n s i t i e s , I:+,+, a n d had t o b e c o r r e c t e d f o r t h e r e s p e c t i v e b a c k g r o u n d s c a t t e r i n g , b I s + c + m a n d Ic+,,,, o r i g i n a t i n g from t h e h i g h p r e s s u r e f u r n a c e (m). T h e s e b a c k g r o u n d i n - t e n s i t i e s w e r e o b t a i n e d from a n i n t e r p o l a - t i o n b e t w e e n two s e p a r a t e e x p e r i m e n t a l r u n s : o n e o f a Cadmium-rod, I : ~ + ~ , m e a s u r e d i n s t e a d o f t h e s a m p l e c e l l i n s i d e t h e h i g h p r e s s u r e f u r n a c e , and a n o t h e r o n e o f t h e

C8- 196 JOURNAL DE PHYSIQUE From t h e s e c o n s i d e r a t i o n s a n d from t h e r e - p r o d u c i b i l i t y o f S(Q) i n s e p a r a t e r u n s w i t h d i f f e r c n t s a m p l e c e l l s a n d f u r n a c e a r r a n g e - m e n t s t h e f o l l o w i n g e r r o r e s t i m a t e r e s u l t s f o r t h e d a t a p r e s e n t e d i n t h e f o l l o w i n g s e c t i o n : a t low t e m p e r a t u r e s t h e u n c e r t a i n - t y o f S(Q) s h o u l d be a b o u t ' 5 % f o r Q > 1 . 3 R - I i n c r e a s i n g t o a b o u t '15% a t t h e h i - g h e s t t e m p e r a t u r e s f o r t h e w h o l e Q - r a n g e . I n r e l a t i o n t o t h i s it i s n o t e w o r t h y t h a t o u r d a t a f o r 350 K a g r e e w i t h i n

t

5 % w i t h c o r r e s p o n d i n g r e c e n t r e s u l t s o f H o w e l l s a n d C o p l e y ( 1 2) f o r Q > I - 3

ji-'.

I 1 1 RESULTS A N D DISCUSSION F i g . 1 g i v e s a s e l e c t i o n f o r d i f f e r e n t tem- p e r a t u r e s a n d d e n s i t i e s o f t h e s t r u c t u r a l r e s u l t s o f t h i s work o n e x p a n d e d l i q u i d r u - b i d i u m

-

s e e a l s o t h e p r e l i m i n a r y p u b l i c a - t i o n ( 1 3 )

-.

I n t h e u p p e r p a r t , t h e s t a t i c s t r u c t u r e f a c t o r , S ( Q ) , i s p l o t t e d , and b e 1 o w t h e c o r r e s p o n d i n g F o u r i e r t r a n s - f o r m

,

t h e p a i r c o r r e l a t i o n f u n c t i o n , g ( R ) , i s shown. F o r a q u a n t i t a t i v e c o m p a r i s o n some s p e c i f i c d a t a a r e summarized a g a i n i n t a b l e 1 . t a b l e 1: C h a r a c t e r i s t i c f e a t u r e s of the experimen- t a l S(Q)-data of expanded l i q u i d rubidium f o r d i f f e r e n t temperatures

T(K)

and densi-

1

t i e s : Q1 (6i- ) = p o s i t i o n o f f i r s t peak i n S(Q) ; S1 (0) = l i n e a r l y ex- trapolated value from S(Q)-data of t h i s work; SZ(0) = calculated according t o the Omstein-Zernike r e l a t i o n from pVT-data

(41

0 3 6 0 1 2 1 5

~ ( 8 )

-

A s f o r t h e c h a n g e o f t h e m i c r o s c o p i c s t r u c - t u r e and s c a t t e r i n g c h a r a c t e r i s t i c s d u r i n g e x p a n s i o n , t h e most s i g n i f i c a n t o b s e r v a - t i o n s a r e : 1 ) The i n t e n s i t y o f t h e f i r s t p e a k i n S ( Q ) i s s t r o n g l y r e d u c e d w i t h d e c r e a s i n g d e n s i - t y , w h i c h m a i n l y r e f l e c t s a l i n e a r d e c r e a - s e o f t h e number o f n e a r e s t n e i g h b o u r s , N 1 , a s c a l c u l a t e d from t h e f i r s t p e a k o f g ( R ) . T h i s l a t t e r c o n c l u s i o n i s d e m o n s t r a t e d s e - p a r a t e l y i n F i g . 2 . 2 ) The p o s i t i o n , Q1

,

o f t h e f i r s t p e a k o f S(Q) d e c r e a s e s o n l y s l i g h t l y w i t h d e - c r e a s i n g d e n s i t y w h i c h b e a r s a d i r e c t r e l a - t i o n t o a n a l m o s t c o n s t a n t n e a r e s t n e i g h - b o u r d i s t a n c e , !I1, d e f i n e d by t h e f i r s t ma- ximum o f g ( R ) - s c e F i g . 2

-.

3 ) F o r d e n s i t i e s below 0 . 6 6 g c m - 3 , a b o u t d o u b l e t h e c r i t i c a l d e n s i t y , t h e s t r u c t u r e i n S ( Q ) i s a l m o s t c o m p l e t e l y s m e a r e d o u t f o r h i g h e r Q - v a l u e s , w h e r e a s a t low Q-va- l u e s a t r e m e n d o u s i n c r e a s e o f t h e s c a t t e - r i n g i s f o u n d . T r y i n g a n O r n s t e i n - Z e r n i k e p l o t f o r t h e 2000 K-curve and f o r Q~ < 0.1 y i e l d s f o r t h e c r i t i c a l c o r r e l a t i o n l e n g t h ,

5 ,

a n a p p r o x i m a t e v a l u e o f 3 . 5

E

( 6 ) . T h i s i s d i r e c t l y c o m p a r a b l e w i t h t h e b e h a v i o u r i n f l u i d a r g o n f o r t h e same re- d u c e d d i s t a n c e from t h e c r i t i c a l t e m p e r a - t u r e , I T

-

T,I

/Tc = 0 . 0 4 , w h e r e

5

'1. 5

8

( 1 4 ) . T h i s g i v e s a f i r s t i n d i c a t i o n , t h a t l o n g r a n g e c r i t i c a l f l u c t u a t i o n s a r e n o t a d e t e r m i n i n g f a c t o r f o r t h e o n s e t o f t h e

f

1

°

Fig.2 Change of t h e microscopic s t r u c t u r e o f li-

C8-198 JOURNAI. DE PHYSIQUE

3

I Fig.3 are due to the ILL, Grenoble, for the neutron beam

Comparison of experimental (-)

and according to the hard sphere model calculated

(--) structure factors, S(Q)

,

1L00 K _{of expanded li-}

quid rubidium;

1700 K _{the hard sphere}

diameter, a,

I

has been fitted to the first ma-

0

1

2

3

4

5

_{ximum of S(Q).}

a

[

A-'

I

-

M-NM

transition region.

4) The simplest modelling of the structural data is that with a hard sphere model, which is presented in Fig.3. Allowing a va- riation of the hard sphere diameter, a , from 4.4

8

near the triple point to about 4

8

at 1700

K

yields a qualitatively satis- factory fit to the experimental curves for Q > 1 R - l . A decrease of a of this magni- tude is reasonable for such a large tempe- rature variation indicating an increasing softness of the repulsive part

of

the Rb- potential. However, at small Q-values clear deviations from the hard sphere model show up. In how far this may be related to chan- ges in the interatomic interaction

-

espe- cially concerning the attractive part

-

is a problem which has to be investigated

facilities and to the DFG

-

W.F. and F.H. - and

&!IT

-

E.Sch. - for financial support. REKE!ENCES

1 U.Even,W.Freyland:J.Phys.F: _- 5, 104 (1975)

2 R.Block,J.B.Suck,W.Freyland,F.Hensel,W.Glaser: in "Liquid Ftetals" ed.R.Evans,D.A.Greenwod, 1977

(Inst. Phys .Conf .Ser.

30,

Bristol)

3 W. Freyland,H. P.Pfeifer ,F.Hensel : in "Amorphous and Liquid Semiconductors" ed. J . Stuke ,W. Bredig

,

1974 (Taylor and Francis, London)

4 G. Franz

,W.

Freyland,F. Flensel

,

these proceedings 5 W.Freyland, Phys.Rev.B

0,

5104 (1979)

6 W.Freyland,Conun.Sol.State Phys. (to be published) and W.Freyland, Habilitationsarbeit, University of hhrburg (1980)

7 W.Freyland,F.Hensel ,W.Glaser: Ber. Bunsenges .phys. Chem. 83, 884 (1979)

_-

8 H.H.Paalmann,C.J.Pings ,J.Appl .Phys.s,2635

(1

962) 9 D.M..Vorth,J.E.Enderby,P.A.Egelstaff, J.Phys.C

(Proc.Roy.Soc.) - 1, 784 (1968)

10 D.F.Page: in "Chemical Applications of Thermal Neutron Scattering", ed.B.T.M.Willis, 1973 [Ox- ford University Press, London)

1 1 W.S.tbwells, ILL Internal Technical Report, 77 HO 46T (1977)

12 W.S.Howells,J.R.D.Copley, priv.comm. (1979) 13 G.Franz,E.Schneider,W.Freyland: in "Liquid and

Amorphous Metals" ed.E .Liischer, NASI (1 979) 14 J.S.Kin,P.W.Schmidt: Phys.Rev.A 10, 2290 (1974). _-

further.

ACKNOWLEDGEMENT